Optical resonators are exemplary electro-optical devices that are often small in size, having diameters on the order of millimeters, and may be used in many optical system applications, including optical sensors for biological and chemical compounds, electro-optical oscillators and modulators, and tunable optical filters. The optical resonators are curved optical waveguides, for example, a cylinder, a sphere, or a toroid within which light is internally reflected at the inner surface of the optical resonator. Optical resonators can support resonator modes of light called whispering-gallery modes (“WGMs”), and thus, are often referred to as whispering-gallery mode resonators. WGMs occur when light having an evanescent wave component travels via internal reflection around the periphery of the optical resonator. The WGMs of optical resonators reside close to the surface of the optical resonator, and undergo total internal reflection. The evanescent waves extend beyond the optical resonator's outer surface and may be coupled into an adjacent optical coupler as long as the optical coupler is located within the extent of the evanescent wave, typically on the order of the light's wavelength.
Many optical resonators which propagate WGMs of light have extremely low transmission loses, and as a result, have a very high quality factor (“Q”). High Q optical resonators are desirable because the higher the Q, the longer the amount of time the internally reflected light will remain within the optical resonator. The ultimate intrinsic Q of the optical resonator (Q0) is limited by the optical losses of the resonator material. Optical resonators having radiuses of 10 to a few hundred micrometers have been produced with Q's in excess of 1×109 (see V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A37, 393 (1989); L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993)). In particular, a Q in excess of 1×1010 was demonstrated for optical resonators, and a Q of 1011 is expected for glass microsphere optical resonators with a resonant wavelength of light at 1550 nanometers, where the intrinsic loss of glass is a minimum.
Coupling to WGMs of the optical resonator can be accomplished through an evanescent wave from an adjacent optical element, i.e., an optical coupler. If light from the optical coupler is over-coupled to the optical resonator, there will be broadening in the WGM output peak due to increased losses at the interface between the optical coupler and the optical resonator. If light from the optical coupler is under-coupled to the optical resonator, there will be less efficient energy transfer from the optical coupler to the optical resonator. Critical coupling occurs when enough energy is coupled from the optical coupler into the optical resonator to compensate for the roundtrip losses of the light propagating through the optical resonator. Coupling losses between the optical coupler and the optical resonator are exponentially dependent upon the distance d between the surface of the optical coupler and the optical resonator ˜exp(−d/r*), where r* is the effective scale length of evanescent field of the resonator for the excited WGM as expressed in the following equation:r*=λ/√{square root over ((4π(nres/nout)2−1))}
where:                λ is the wavelength of light evanescently coupled between the optical coupler and the optical resonator;        nres is the index of refraction of the optical resonator; and        nout is the index of refraction outside the surface of the optical resonator.        
If the optical coupler contacts the optical resonator, too much of the light is evanescently coupled out from the optical resonator resulting in a low Q. Also, if the optical coupler is positioned far, more than three wavelengths, from the optical resonator, coupling of light between the optical resonator and the optical coupler becomes difficult. Thus, accurate positioning of the optical coupler relative to the optical resonator is critical to the efficiency of the optical system.
Optical couplers can be configured in various forms including those shown by example in FIGS. 1 and 2 which include cross-sectional views, not shown to scale, of two different types of optical couplers 10 and 12. In FIGS. 1 and 2, each optical coupler is positioned adjacent to and spaced away from a cylindrical or spherical optical resonator 16 and 18 by a distance “d”, which in practice is roughly on the order of the wavelength of the light to be evanescently coupled into or out from the optical resonator. Typically, d ranges in value from approximately 0.1 to 3 times the wavelength of the light. While not shown in FIGS. 1 and 2, the optical resonator also may be toroidal in shape.
FIG. 1 shows an optical fiber coupler 10 that includes a core 22 and a cladding layer 24. The end of the optical fiber coupler closest to the optical resonator 16 has a flat polished surface 26 through which light is evanescently coupled into and out from the optical resonator. Similarly, FIG. 2 shows a prism coupler 12, which is the traditional method of coupling light into an optical resonator, having a flat surface 28 through which light is evanescently coupled into and out from the optical resonator 18. In FIGS. 1 and 2, incident light travels through the optical coupler as indicated by the straight arrows 30 and 32, respectively, and internally reflected light travels around the periphery of the optical resonator as shown by the curved arrows 34 and 36, respectively.
Because the optical resonator and optical coupler are small in size they may be integrated within small housings or devices that can be incorporated into various optical or electro-optical systems. However, for many applications, especially where on-chip integration is desired, coupling with a prism 12 and the associated lenses (not shown) are not practical, and coupling directly from a waveguide, for example an optical fiber 10, to the optical resonator is desired as shown in FIG. 1 (see V. S. Iltchenko, X. S. Yao, and L. Maleki, Opt. Lett. 24, 723 (1999)).
The basis for optical coupling using a waveguide is in phase matching of the field of the waveguide to the field in the optical resonator's WGM which is accomplished by cutting the waveguide at the angle Φ as shown in FIG. 1. In order to satisfy the phase matching requirement Φ=arc sin(nres/nwg), where nres is the effective index of refraction for azimuthal propagation of the WGMs as closed waves circulating in a microsphere optical resonator, and nwg is the effective index of refraction for the light guided by the waveguide.
Even though the use of a waveguide to couple light into an optical resonator is advantageous in that it eliminates the need for columnating and focusing optics that is commonly required for prism couplers, the precision cut of the waveguide to create the required angle is difficult to implement. This is especially true in the case of semiconductor waveguides where efficient growth and the cleave angle relate to the orientation of the waveguide material. In addition, the above mentioned angle phase matching scheme is not suitable for cases in which the indices of refraction of the waveguide and the optical resonator are significantly different, for example, when the waveguide is a silicon optical fiber having a core index of refraction of 1.46 and the optical resonator is made of lithium niobate having an index of refraction of 2.06.
Therefore, there is a need for an optical coupler for coupling evanescent waves into and out of optical resonators that does not require the precise angle cut of the waveguide. Also, there is a need for an optical coupler that can couple evanescent waves even though the indices of refraction of the waveguide and the optical resonator are significantly different.